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arXiv · 1708.07331

On the orders of the non-Frattini elements of a finite group

Andrea Lucchini
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Abstract

Let $G$ be a finite group and let $p_1,\dots,p_n$ be distinct primes. If $G$ contains an element of order $p_1\cdots p_n,$ then there is an element in $G$ which is not contained in the Frattini subgroup of $G$ and whose order is divisible by $p_1\cdots p_n.$

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Andrea Lucchini. 2017-08-24. On the orders of the non-Frattini elements of a finite group. https://arxiv.org/abs/1708.07331

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